/sci/ - Science & Math

>>9655516
It's pi.

Area of the spherical cap is
A=2*pi*a^2*(1-cos(t)).

sin(t/2)=1/2a (pic related)
cos(t)=cos(2*(t/2))=cos^2(t/2)-sin^2(t/2)
=1-2*sin^2(t/2)
=1-2*(1/2a)^2
=1-1/2a^2
=>1-cos(t)=1/2a^2

=> A=2*pi*a^2*(1/2a^2)
= pi